Laws or motions and a truck that won't move.

[azertyq]

I have been bothered with a problem that I know should not be monopolizing as much time as it has. It just annoys me how I keep missing the little thing that would make the problem more understandable.

Anyways, here is the problem, with my attempt of a solution:

a tow truck pulls on a car with a 2500N force directed along the cable used for towing. The purpose of the problem is to find the force in the members of the 'towing crane' used, assuming that both the car and the truck are not moving. (the attached FBD should make more sense.. sorry)

Here are the calculations and results I got:

(sum of forces F) F = ma = 0 // at the point C where the three forces are joined

--> Fx= 0 and Fy=0


F1= -2500* cos(40) i - 2500*sin(40) j // finding the vector corresponding to each force

Fa= - Fa j

Fb= Fb*cos(50) i - Fb*sin(50) j

Fx= [ (-2500* cos(30) + Fb*cos(50)]= 0 //applying the equilibrium equation
--> Fb = 2500* cos(30) / *cos(50)
Fb= 1632 N
Fy= [ - 2500*sin(30) - Fa - Fb*sin(50)] = 0

--> Fa = -(2500*sin(30) + Fb*sin(50))
Fa = -(2500*sin(30) + 2979*sin(50))
Fa= 3214 N


It seems logic to me that it'd be the correct resolution path, but according to the textbook, the correct values for Fa and Fb are

Fa= 3.83kN and Fb=3.37kN


Quite different from what I got indeed.

If anyone could help me with this problem, it'd be great. I tried. I really did. :(

 

[azertyq]

I feel kind of stupid after finding out that I had jut made a computation error.
I guess things like that are bound to happen. >_<
lol

Sorry to have bothered you guys.

 

[thepatientmental]

Thank you for sharing your problem and your attempted solution. It can be frustrating when we put in effort to solve a problem and still come up with incorrect results. In this case, it seems like there may be a mistake in your calculations or assumptions. It is always a good idea to double check your work and make sure you are using the correct formulas and units.

In terms of laws or motions, there are several principles that can help us understand why the truck is not moving in this scenario. One is Newton's First Law of Motion, which states that an object at rest will remain at rest unless acted upon by an external force. In this case, the truck is not moving because the forces acting on it are balanced, resulting in a net force of zero.

Another relevant concept is equilibrium, which is when all forces acting on an object are balanced and there is no net force. In your solution, you correctly identified that the sum of forces in the x and y directions should be equal to zero for equilibrium to be achieved. However, it is possible that there was a mistake in your calculations that led to the incorrect values for Fa and Fb.

In the end, it is important to remember that mistakes and challenges are a normal part of problem-solving. It may be helpful to go back and review the problem, check your calculations, and seek help from a teacher or classmate if needed. Keep persevering and you will eventually find the solution.